Field of Invention
The present invention relates to a method for processing a 3-dimensional mesh, and more particularly to a method for generating a hexahedral mesh based on a closed-form polycube.
Description of Related Arts
Hexahedral meshes have a wide range of applications in computer graphics and in industries such as CAD, physical simulation, geometrical construction, and so on. However, there are still many problems in automating the generation of hexahedral meshes, such as the low degree of automation and the inability to avoid global degradation, and the resulting hexahedral mesh quality is not high. Conventionally, fully automatic hexahedral mesh generation is still a big challenge.
The conventional hexahedral mesh generation methods have their own shortcomings:
1, For a hexahedral mesh generation method based on polycubes, it is necessary to assume that the initial orientation of the model is good, see [Gregson et al. 2011 All-hex mesh generation via volumetric polycube deformation In Computer graphics forum, vol. 30, Wiley Online Library, 1407-1416]. Furthermore, the method lacks user control, see [Gregson et al. 2011 All-hex mesh generation via volumetric polycube deformation In Computer graphics forum, vol. 30, Wiley Online Library, 1407-1416. Tarini et al. 2004 Polycube-maps. In ACM Transactions on Graphics (TOG), vol. 23, ACM, 853-860].
2, For complex models, such as high genus and models with complex feature line constraint, it is impossible to get a high-quality hexahedral mesh based on polycube. [Huang et al 2014. L1 based construction of polycube maps from complex shapes. ACM TOG 33, 3, 25:1-11] discloses a polycube generation method based on L1 optimization, which can be used for hexahedral mesh generation. However, the method is based on the global uniform frame field, and the quality of the hexahedral mesh is not high.
3, [Li et al. 2012. All-hex meshing using singularity-restricted field. ACM TOG 31, 6, 177:1-11] discloses a hexahedral mesh generation method based on a three-dimensional frame field with singularity. However, the method requires a grid modification operation for many degradations, and has poor robustness, leading to difficulty in handling of complex global degradation.